Biquadratic and ring exchange interactions in orthorhombic perovskite manganites

TL;DR

This study uses advanced electronic structure calculations to identify higher order magnetic interactions, like biquadratic and ring exchanges, as key to understanding the complex magnetism in orthorhombic manganites.

Contribution

It demonstrates that higher order magnetic interactions are essential for accurately modeling magnetism in o-RMnO3 compounds, beyond simple Heisenberg models.

Findings

Higher order interactions are significant in TbMnO3.

Deviation from Heisenberg behavior is not due to spin-orbit coupling.

Biquadratic and ring exchanges improve magnetic modeling.

Abstract

We use ab initio electronic structure calculations within the generalized gradient approximation (GGA+U) to density functional theory (DFT) to determine the microscopic exchange interactions in the series of orthorhombic rare-earth manganites, o-$R$MnO$_3$. Our motivation is to construct a model Hamiltonian (excluding effects due to spin-orbit coupling), which can provide an accurate description of the magnetism in these materials. First, we consider TbMnO$_3$, which exhibits a spiral magnetic order at low temperatures. We map the exchange couplings in this compound onto a Heisenberg Hamiltonian and observe a clear deviation from the Heisenberg-like behavior. We consider first the coupling between magnetic and orbital degrees of freedom as a potential source of non-Heisenberg behavior in TbMnO$_3$, but conclude that it does not explain the observed deviation. We find that higher order magnetic interactions (biquadratic and four-spin ring couplings) should be taken into account for a proper treatment of the magnetism in TbMnO$_3$ as well as in the other representatives of the o-$R$MnO$_3$ series with small radii of the $R$ cation.